Rit (Vísindafélag Íslendinga) - 01.06.1931, Blaðsíða 10

10
first five equations for the case where a5 = aG = a7 = . . .
= & = &=... = 0.
Thus we get from (13) the following relations:
a0+^2a2+^3a3+(3^22+^4)a4+/?l + 3^2/4 + 4^3//4 0 (I6a)
^2al+^3a2 + (3^22 +^4) a3 + (1 OVs+^s) a4+A>+ 3^2
+4/.3^3+(15^22+5^4)/?4 = 0 (16b)
^3al+(2^22++)a2 + (9^3+^5)a3
+ (1 2/.2 3 + 14^4 + 10+2 + 'lö) a4+2^2 A + 4^3 /?2
+ (12^22 + 5^4)i®3 + (56^2^3 + 6^5)^4 = 0 (16c)
+al + (6?+3 +^s)a2 + (6^23 + 1 2^+4 + 9^32 +^6)a3
+ (7 2^22^3 + 18/-2Á', + 34^3^4+^?)a4 + 3^3/?l + (6^22 + 5+/J2
+ (45^2^3 + 6/.5)^3 + (60/-23 + 90),2^4+66?.32 + ?ig)/^4 = 0 (16d)
/'•5al + (8A2/.4+6/.32 + Ao)a2 + (36X22/-3+15A2^5 + 301.3?i4 + A.7)a3
+ (24/.24+120/.22A4+180?,2^32 + 221.2/.6 + 52^.3^.5 + 34/42+A8)a4
+4?i4/Si+(241.2?^+6Á5)/?2+(24Á23+72Á2/4+54/.32+776)/?3
+(432/,22A3+ 132?.2?.5+256A3?.4+ = 0 (16e)
This system of equations may easily be extended to em-
brace more equations, but, for our present purposes, these
will suffice generally.
We observe that a0 only occurs in the first equation (16a)
while p0 is only found in (16b). By this procedure we have,
therefore, succeeded in separating two of the unknown
quantities.
Now we proceed to illustrate the application of the
equations (16a) to (16e) in some simple cases:
A. Let a2=a3=a4=|Si=jd2=/Ss=^4 = 0 then we have:
a0 — 0, A.2ai+Ai — 0,
?-3al = 0, A.4al = 0, ?.5al = 0.
Hence fa = — h0 = . .. = 0 = ao, /?o = — ?-2ai
and therefore:
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